New algorithms for sampling and diffusion models

TL;DR

This paper introduces new algorithms for sampling and diffusion models based on stochastic differential equations, offering improved convergence and applicability without regularity assumptions, demonstrated through numerical experiments.

Contribution

The paper presents novel sampling and diffusion algorithms derived from SDE theory, with explicit convergence rates and dimension-free guarantees, applicable to both generative modeling and optimization.

Findings

Effective sampling without regularity assumptions

Dimension-free convergence guarantees

Numerical experiments confirm method effectiveness

Abstract

Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the concept of the reverse diffusion process, widely adopted in diffusion generative models. Additionally, we derive the explicit convergence rate based on the smooth ODE flow. For diffusion generative models and sampling, we establish a dimension-free particle approximation convergence result. Numerical experiments demonstrate the effectiveness of our method. Notably, unlike the traditional Langevin method, our sampling method does not require any regularity assumptions about the density function of the target distribution. Furthermore, we also apply our method to optimization problems.